BOS: Model-based clustering of multivariate ordinal data relying on a stochastic binary search algorithm

We design the first univariate probability distribution for ordinal data which strictly respects the ordinal nature of data. More precisely, it relies only on order comparisons between modalities. Contrariwise, most competitors either forget the order information or add a nonexistent distance information. The proposed distribution is obtained by modeling the data generating process which is assumed, from optimality arguments, to be a stochastic binary search algorithm in a sorted table. The resulting distribution is natively governed by two meaningful parameters (position and precision) and has very appealing properties: decrease around the mode, shape tuning from uniformity to a Dirac, identifiability. Moreover, it is easily estimated by an EM algorithm since the path in the stochastic binary search algorithm is missing. Using then the classical latent class assumption, the previous univariate ordinal model is straightforwardly extended to model-based clustering for multivariate ordinal data.

Author
Christophe Biernacki and Julien Jacques
Date of publication
2016-03-07 15:32:47
Maintainer
Julien Jacques <julien.jacques@univ-lyon2.fr>
License
GPL (>=2)
Version
1.0

View on R-Forge

Man pages

AERS
French university evaluations
BOS-package
Model-Based Clustering of Multivariate Ordinal Data
clustMultiBOS
Function to cluster multivariate ordinal data

Files in this package

BOS/DESCRIPTION
BOS/NAMESPACE
BOS/R
BOS/R/ordinal-clustering.R
BOS/data
BOS/data/AERS.rda
BOS/man
BOS/man/AERS.Rd
BOS/man/BOS-package.Rd
BOS/man/clustMultiBOS.Rd